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lawyer [7]
3 years ago
9

Solve the compound inequality -5x<10 and x+5>2

Mathematics
1 answer:
Phantasy [73]3 years ago
8 0
-5x < 10...divide both sides by -5, changing the inequality sign
x > 10/-5
x > -2

x + 5 > 2...subtract 5 from both sides
x > 2 - 5
x > -3
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Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the me
mel-nik [20]

Answer:

The perimeter of the base of the birdhouse is 36 units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?

step 1

Find the measure of the interior angle

Let

x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

so

x+y=180^o ----> equation A

we have that

the measure of the interior angle is twice the measure of the exterior angle

so

x=2y ----> equation B

substitute equation B in equation A

2y+y=180

y=60^o

so

x=120^o

That means-----> The figure is a regular hexagon

step 2

Remember that

The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon

Let

b ----> the length side of the hexagon

so

b=12/2=6\ units

The perimeter of the hexagon is given by the formula

P=6b

substitute

P=6(6)=36\ units

3 0
3 years ago
What law can be used to determine that the conclusion is valid based on the given statements
ryzh [129]

Answer:

A. Law of detachment

Step-by-step explanation:

The Law of detachment implies that when one condition is fulfilled the other cannot be and vice versa, then it is made the conclusion.

This condition is made the conclusion.

The Acute and Obtuse are detached of each other.

The acute angle is one in which the value of the angle is less than 90 degrees and obtuse angle is one in which the angle is greater than 90 degrees but less than 180 degrees.

Thus angles less than 90 degrees are acute and greater than 90 degrees are obtuse.

The conclusion of the given statement  is valid based on the law of detachment as the condition has been made a conclusion.

8 0
3 years ago
A cylinder has a volume of 245 cubic units and a height of 5 units. The diameter of the cylinder is
Vikki [24]

Answer:

The diameter is twice that, or approx. 7.90 units.

Step-by-step explanation:

the equation for the volume of a cylinder of radius r and height h is

V = πr²h.  Here we need to calculate the diameter after having found the radius.  Solving V = πr²h for r², we get:

           V

r² = -----------

         πh

Substituting the given values, we obtain for r² the following:

         145 units³

r² = ------------------------  = 15.6 units²

       3.14159(5 units)

Taking the square root of both sides, we get:

r = √15.60, or approx. 3.95 units.

The diameter is twice that, or approx. 7.90 units.

3 0
3 years ago
Read 2 more answers
A $10 decrease followed by a $15 increase
Leto [7]
That’s not the full question but if it was it would be greater bc 10 - 10=0 but 10-10+15 would equal 15 instead of 10
3 0
3 years ago
Different shapes are drawn on cards and then the cards are placed in a bag. The number of cards for each shape is shown in the t
Verdich [7]
This question was posted almost a week ago, and I am not sure if you still need the answer, but I'll explain it.


The total number of all of the shapes were placed in the bag are equal to 100. The number comes from adding 32+20+48=100.
This is our total number and will be the denominator.
There are a total of 32 cards which have a hexagon, this number will be our numerator.

So far we have 32/100 , but this is not simplest form.

Next to reduce the fraction, the GCF must be found.

32: 1, 2, 4, 8, 32
100: :
8 0
3 years ago
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